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An existence theorem for Cournot-Walras equilibria in a monopolistically competitive economy
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An existence theorem for Cournot-Walras equilibria in a monopolistically competitive economy

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  • Shirai, Koji

Abstract

We establish an existence theorem for Cournot-Walras equilibria in a monopolistically competitive economy. Instead of the traditional approach which depends on Kakutani's fixed point theorem, we employ the theories of aggregative games and best reply potential games. We show that, if there exists a representative consumer, under some conditions on preferences and production technologies, the profit maximization game is a (pseudo) best reply potential game. Hence, the existence of the equilibria is proved independently of the well known convex-valued assumption on the best responses. Although our assumptions result in the additive separability on a utility function of a representative consumer, the existence of increasing returns and indivisible productions can be allowed. In our model, it is shown that the game played by firms exhibits strategic substitutes whether the products of firms are substitutes or complements, and this plays an important role for the existence of the equilibria.

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  • Shirai, Koji, 2010. "An existence theorem for Cournot-Walras equilibria in a monopolistically competitive economy," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1093-1102, November.
    • Handle: RePEc:eee:mateco:v:46:y:2010:i:6:p:1093-1102
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    Cited by:

    1. Alex Dickson & Simone Tonin, 2021. "An introduction to perfect and imperfect competition via bilateral oligopoly," Journal of Economics, Springer, vol. 133(2), pages 103-128, July.
    2. Michael Zierhut, 2021. "Generic regularity of differentiated product oligopolies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 341-374, February.
    3. Michael Zierhut, 2021. "Indeterminacy of Cournot–Walras equilibrium with incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 81-114, February.

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